A topological approach to Wilson’s impossibility theorem

Abstract

We will present a topological approach to Wilson’s impossibility theorem [Wilson, R.B., 1972. Social choice theory without the Pareto principle. Journal of Economic Theory 5, 478–486] that there exists no non-null binary social choice rule which satisfies transitivity, independence of irrelevant alternatives, non-imposition and has no dictator nor inverse dictator. Our research is in line with the studies of topological approaches to discrete social choice problems initiated by [Baryshnikov, Y., 1993. Unifying impossibility theorems: a topological approach. Advances in Applied Mathematics 14, 404–415]. This paper extends the result about the Arrow impossibility theorem shown in [Tanaka, Y., 2006. A topological approach to the Arrow impossibility theorem when individual preferences are weak orders. Applied Mathematics and Computation 174, 961–981] to Wilson’s theorem.